1. Field of the Invention
The present invention relates to a technique for the optimal design of a conveying path for a paper sheet based on a computer-simulation analysis of the paper sheet's behavior in a copy machine, a printer, or the like.
2. Description of the Related Art
In the design of a conveying path for paper sheets in a copy machine, a laser beam printer (LBP), or the like, the number of processes required for manufacturing test products and performing tests and the time and cost of development can be reduced by analyzing the functions of the conveying path under various conditions.
As an example of a technique for simulating the behavior of a flexible medium (a sheet-shaped recording medium such as a piece of paper and a film) in a conveying path, Japanese Patent Laid-Open Nos. 11-195052 and 11-116133 disclose design support systems in which the resistance and the contact angle between the flexible medium and a guide are evaluated by modeling the flexible medium with finite elements using the finite element method, and determining whether the flexible medium is in contact with guides and rollers in the conveying path, by numerically solving a dynamic equation.
In addition, Dynamic Analysis of Sheet Deformation Using Spring-Mass-Beam Model is also disclosed (Kazushi Yoshida, Transaction of the Japan Society of Mechanical Engineers, Vol. 63, No. 615C(1997-11), P230-236 Thesis No. 96-1530).
The motion of the flexible medium can be determined by deriving a dynamic equation of the flexible medium modeled with discrete finite elements or mass-spring elements, dividing the analysis time interval into time steps with a finite width, and successively determining unknown values of the acceleration, the speed, and the displacement for each time step by numerical time integration starting from time zero. For example, the Newmark β method, the Wilson θ method, the Euler method, the Kutta-Merson method, etc., are known in the art.
In the known design support systems for the conveyance of the flexible medium, the flexible medium is modeled with a finite number of elements (finite elements or mass-spring elements). A coefficient of friction μ which depends on the difference between the speed of conveyor rollers and the speed of the flexible medium, as shown in FIG. 2, is defined for each of the representative points of the elements (mass points if the elements are the mass-spring elements), and the motion of the flexible medium is calculated under a condition including a conveying force obtained as the product μN of the coefficient of friction μ and the normal force N.
A motion-calculation method used in the known design support systems for the conveyance of the flexible medium will be described below with reference to FIGS. 17 to 19. FIGS. 17 to 19 show a typical manner in which the flexible medium is conveyed. In FIG. 17, reference numerals 31, 32, and 33 denote mass points, reference numerals 34 and 35 denote springs positioned between the mass points, reference numeral 36 denotes a drive conveyor roller, and reference numeral 37 denotes a driven conveyor roller. Similarly, in FIGS. 18 and 19, reference numerals 41, 42, and 43 and reference numerals 51, 52, and 53 denote mass points.
In this calculation method, the difference ΔV between the conveying speed Vr of the rollers and the conveying speed Vp of the medium at the time when the mass point 31 reaches the contact point (nipping region) between the rollers is calculated as follows:ΔV=Vr−Vp
Then, the coefficient of friction μ is determined from FIG. 2 on the basis of the calculated ΔV, and the conveying force F=μN is calculated on the basis of a pressing force N applied by the driven roller 37. Thus, the conveying force F is applied to the mass point 31.
The conveying force F further conveys the medium, and the state shown in FIG. 18 is obtained. The conveying force F calculated on the basis of the state shown in FIG. 17 is assumed to be applied continuously to the mass point 41 until the next mass point 42 enters the nipping region. As shown in FIG. 19, when the next mass point 52 enters the nipping region, the conveying force F is updated and a new conveying force F′ is calculated on the basis of Vr and Vp at this time.
When the above-described calculation method is used, a large force is assumed to be applied to the mass point even when ΔV is small, and therefore the calculation result of the medium's speed greatly varies. In addition, the force applied is assumed to be constant while the state of the medium changes from that shown in FIG. 17 to that shown in FIG. 19. Therefore, even when the peripheral speed Vr of the rollers is set constant, the conveying speed Vp of the medium varies periodically unless the number of elements into which the medium is divided is considerably increased and the width of the time steps is considerably reduced.
In addition, if a relatively large external force is suddenly applied to the medium from a guide or another roller, etc., when no mass point is in the nipping region, as shown in FIG. 18, the medium cannot resist such a force and false slipping occurs between the medium and the rollers.